Análise semiótica de componentes da aprendizagem em atividades de modelagem matemática no 8º ano do ensino fundamental

Abstract

For the present research, we are based on Mathematical Modeling as a pedagogical alternative and on the Learning Components that are subsidized in the Theory of Registers of Semiotic Representations as a theoretical framework of didactics of Mathematics. We understand that mathematical modeling activities can be organized according to cycles in which phases are present: integration, mathematization, interpretation of results and validation. With this, the research aimed to investigate "How are the learning components evidenced in the phases of mathematical modeling activities developed by students of the 8th year of Elementary School?". Based on this objective, we present the description and analysis of two mathematical modeling activities developed in two classes of the 8th grade of elementary school in two private schools located in Londrina-PR. The activities were selected considering greater student participation, in order to subsidize our qualitative analysis of an interpretative nature. For that, the data collected came from written records, photos, video and audio recordings and the teacher-researcher's logbook. The analysis of the activities showed specificities regarding the modeling cycle that the students went through. In the activity “Renovation of the court”, the students followed the phases of the cycle in a linear way, while in the activity “Average time of use of cell phone” there were comings and goings. However, the learning components highlighted were the learning: conceptual, algorithmic, strategic and communicative. Conceptual learning is evident when a concept constructed by the student is perceived and he is able to identify it, represent it, transform it and use it appropriately. Algorithmic learning is related to the student's ability to respond to operations, use calculations, apply formulas, and also use convenient tools to solve questions. When the student realizes that the process is more important than the product and the search for strategies to solve a problem becomes evident, these are characteristics of strategic learning. Finally, communicative learning was evidenced as students communicate (whether through speech, writing, gestures) their mathematical ideas in order to justify them. With the analysis of mathematical modeling cycles, and with the purpose of highlighting the learning components that are present in the development phases of modeling activities, we can highlight two categories: the learning components in relation to the problem situation (in the interaction and transition from interaction to mathematization; and in the interpretation of results and validation) and the learning components in the mathematical approach to the problem (during mathematization and resolution). Based on this research, we developed an educational product that aims to bring suggestions to teachers in the final years of Elementary School for the development of Mathematical Modeling activities.